Find the exact global maximum and minimum values of the function g(x)=3x−x2−7 if its domain is all real numbers. global maximum at x= global minimum at x=

Question

Calculus, please show steps, I need to understand how to work through this problem..

Answer 1

g(x) = -x² + 3x - 7, a downward opening parabola. It has a maximum at the vertex.

Two ways to do this.

g'(x) = -2x + 3

0 = -2x + 3

-3 = -2x

3 / 2 = x, now substitute x and calcalate y/2

Or

0 = -(x² - 3x + (-3/2)²) + 7 + (9/2), Completion of the Square

0 = -(x - (3/2))² + (23/2)